1. ModelingV(D)J recombination in lymphocyte T development, the main mechanism for the diversity and tolerance of the immune response. The failure of this process may be
related with the loss of immune tumor control and autoimmune diseases.

3. Modeling of intermittent events for systems closed to a threshold. With particular applications to fusion
plasma physics (the so called "blobs", local disruption events taking place at the electromagnetic transport barriers inside a tokamac).

Abstract. This paper introduces a Markov chain approach that allows a rigorous analysis of agent based opinion dynamics as well as other related agent based models (ABM). By viewing the ABM
dynamics as a micro description of the process, we show how the corresponding macro description is obtained by a projection construction. Then, well known conditions for lumpability make it
possible to establish the cases where the macro model is still Markov. In this case we obtain a complete picture of the dynamics including the transient stage, the most interesting phase in
applications. For such a purpose a crucial role is played by the type of probability distribution used to implement the stochastic part of the model which deﬁnes the updating rule and governs the
dynamics. In addition,
we show how restrictions in communication leading to the co–existence of diﬀerent opinions follow from the emergence of new absorbing states. We describe our analysis in detail with some speciﬁc
models of opinion dynamics. Generalizations concerning diﬀerent opinion representations as well as opinion models with other interaction mechanisms are also discussed. We ﬁnd that our method may
be an attractive alternative to mean–ﬁeld approaches and that this approach provides new perspectives on the modeling of opinion exchange dynamics, and more generally of other ABM.

Abstract. We analyze the dynamics of agent based models (ABMs) from a Markovian
perspective and derive explicit statements about the possibility of linking a
microscopic agent model to the dynamical processes of macroscopic observables
that are useful for a precise understanding of the model dynamics. In this
way the dynamics of collective variables may be studied, and a description of
macro dynamics as emergent properties of micro dynamics, in particular during
transient times, is possible.

NEW!

Interplay of turbulence bursts and transport barriersanalyzed in term of combined stochastic processes

The interplay of large bursts of turbulent transport or blobs with regions of vanishing turbulence is a complex system that can eventually generate transport barriers when the majority of blobs
are trapped in these weak turbulence regions. We present 2 models where stochastic processes are combined to recover the physics of this interaction. The main stochastic variables are the
barrierwidth and the spreading distance of the blobs within the barrier together with their level of correlation.

We predict that for a class of Probability Distribution Function of these stochastic variables, the PDF of the escaping blobs will exhibit heavy tails, either exponential for a leaky barrier, or
with power laws, for a tight barrier. Two-dimensional nonlinear ﬂuid simulations of edge turbulence in tokamak plasmas bearing analogy with Rayleigh-Benard turbulence in neutral ﬂuids – are used
to supporte these stochastic models. The PDF of the blob penetration into the barrier is estimated as well as that of the barrier width for two diﬀerent barriers generated in the plasma boundary
layer. One can show that in the case of a barrier generated by external biasing – leading to an external radial electric ﬁeld shear – the stochastic model predicts a leaky barrier with an
exponential PDF of escaping blobs in agreement with the simulation data.